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line from arc midpoint perpendicular to a side

Source: Sharygin Geometry Olympiad 2016 Final Round problem 2 grade 8

July 22, 2018
geometryarc midpointcircumcircleperpendicularparallelogram

Problem Statement

A circumcircle of triangle ABCABC meets the sides ADAD and CDCD of a parallelogram ABCDABCD at points KK and LL respectively. Let MM be the midpoint of arc KLKL not containing BB. Prove that DM⊥ACDM \perp AC.
by E.Bakaev
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